Geodesic
Diagonal Reduction Algebras of $\mathfrak{gl}$ Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 27-49

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Several general questions concerning a reduction algebra, namely, rings of definition and the algorithmic efficiency of the set of ordering relations, are discussed. For reduction algebras related to the diagonal embedding of the Lie algebra $\mathfrak{gl}_n$ into $\mathfrak{gl}_n\oplus\mathfrak{gl}_n$, a stabilization phenomenon is established and a complete set of defining relations is given.
Keywords: reduction algebra, extremal projector, ordering relations. 
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     author = {O. V. Ogievetskii and S. M. Khoroshkin},
     title = {Diagonal {Reduction} {Algebras} of $\mathfrak{gl}$ {Type}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a2/}
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O. V. Ogievetskii; S. M. Khoroshkin. Diagonal Reduction Algebras of $\mathfrak{gl}$ Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 3, pp. 27-49. http://geodesic.mathdoc.fr/item/FAA_2010_44_3_a2/